An optimum Hamiltonian for non-Hermitian quantum evolution and the complex Bloch sphere

Abstract

For a quantum system governed by a non-Hermitian Hamiltonian, we studied the problem of obtaining an optimum Hamiltonian that generates nonunitary transformations of a given initial state into a certain final state in the smallest time $\tau$. The analysis is based on the relationship between the states of the two-dimensional subspace of the Hilbert space spanned by the initial and final states and the points of the two-dimensional complex Bloch sphere.

14 pages, 8 figures

References in corpus (8)

• Faster than Hermitian Quantum Mechanics
• Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
• Projective Hilbert space structures at exceptional points
• On optimum Hamiltonians for state transformations
• Open system of interacting fermions: Statistical properties of cross sections and fluctuations
• The quantum brachistochrone problem for non-Hermitian Hamiltonians
• On Existence of a Biorthonormal Basis Composed of Eigenvectors of Non-Hermitian Operators
• Comment on the Quantum Brachistochrone Problem

Cited by in corpus (4)

• Probing CPT violation in meson mixing by non-cyclic phase
• Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution
• Exceptional points and quantum correlations in precise measurements
• The stability and energy exchange mechanism of divergent states with real energy